Question

How do you derive the expression e2=p2c2+(mc2)2?

Answer 1

Use :

\(E=\gamma mc^2\)
\(p=\gamma mv\)
\(\gamma =(1-v^2/c^2)^{1/2}\)

Write \(p^2c^2 +m^2c^4\) , factorise \(\gamma ^2m^2c^4\), and simplify.

Answer 2

@Vincent-Lyon.Fr I thought that's called verify.

Without using some deep maths, I guess using those equations and try to eliminate v is the simplest way to derive the relation.

Answer 3

Yes, but you must eliminate both v AND \(\gamma\), which makes the derivation a bit more complicated. That's why I preferred verification.

As a mathematical proof, they have the same validity.